where he concludes, again (as previously concluded by other authors), by other arguments, that the density must equal the density that makes (3D) space flat. He needs to "renormalize" the bare mass by a factor of 11/2 . Mmmmmmm

Einstein did not in the formal sense "incorporate" Mach's Principle, but he named it that and it is doubtful he could have invented GR without it. Certainly GR is consistent with it. The best source for the history of the thing is one of the editors in this book, Julian Barbour; though Woodward give a good bit of the history as well.

If I understand correctly, the key point is that the density parameter needs to be of order unity (various approximations seem to deviate from exact unity by different factors). And according to WMAP (and more recently Planck), the density parameter is basically one. Why this is so, precisely, would seem to be a separate question.

Dark matter and dark energy have been detected, in a sense. That's all they are, really; labels for detected behaviours, with no accepted theory attached. Dark matter = something is gravitating, and we can't see it. Dark energy = the universe is accelerating, therefore something must be causing it to do so. It does not seem unreasonable to me to expect whatever is causing these effects to also participate in (or otherwise modify the nature or magnitude of) a Machian gravinertial interaction.

If a major theoretical overhaul occurs, similar to what happened with Copernicus or Einstein, we can reevaluate, but given what we know now, it seems Sciama's idea is plausible.

It does seem a point in its favour that it was formulated before unconnected, uninterested scientists made the observations that established it as physically tenable... Maybe it's just a misleading coincidence - but in that case, don't we have to explain why the predicted inertia-like gravelectric forces aren't in evidence, or else show that they disappear when the Einstein field equations are used without approximation? These forces seem to result directly from calculations using conventional gravity theory, without any proprietary special sauce added to get them to appear...

A) on one hand positive mass attracts all masses, including a positive mass attracting a negative mass.

B) on the other hand Bondi also concluded that a negative mass repels all masses, so it repels a positive mass.

Bondi concluded that as the negative mass tries to get closer to the positive mass, because of A), while the positive mass is repelled from the negative mass because of B), what really happens is that the negative mass chases the positive mass across the universe at an ever accelerating speed.

Therefore, he agrees with Sciama in that negative mass would be extremely difficult to find.

Woodward has never suggested we can alter the rest mass of particles, but rather only of bulk mass items that store Mach Effects or mass fluctuations in the interatomic energy bonds. In fact, all bulk matter stores delta mass during deformation, since deformation changes the energy in these bonds and energy = mass X c^2.

I was wondering how much energy was stored within the cavity (truncated frustum) so have been (off and on) looking at math for which I have absolutely no background beyond undergraduate course work. Using the input power and Q-factors given, I calculate that the RF wave B field and E field has energy like:

B field range from 0.27 to 0.62 tesla, andE field range from 80.4 to 184.8 Mv per metre.

Are these reasonable values?

I also calculated that the energy mass of the RF wave ranges from 0.00064 to 0.0034 micrograms.

At this point I don't know what to do with these numbers but maybe someone will find them interesting.

We know from the "Anomalous Thrust ..." report that the COMSOL finite element calculations display a maximum Electric field of 47189 Volts per meter (p. 10, Fig. 14). I couldn't find any numerical information given for the Electric Field results from COMSOL for the Tapered Cavity.

Also, you may find something useful for comparison in FIg. 16 of the report, for the predicted and actual gain (S21), as attached here (vertical scale: Amplitude (dB); horizontal scale: frequency):

(The numbering convention for S-parameters is that the first number following the S is the port where the signal emerges, and the second number is the port where the signal is applied. S21 is a measure of the signal coming out port 2 relative to the RF stimulus entering port 1: the ratio of transmitted to incident voltage signals. S21 is the forward complex transmission coefficient)

It is apparent that the comparison from this COMSOL analysis to the actual results is not that great...

I could very easily be making an error in my calculations - BUT - Fig. 14 is for the Cannae Cavities while my calculations address the tapered frustum. The paper doesn't give a Q-factor for the Cannae Cavities so I can't do a calculation to check myself with that example. On the other hand, I can do a calculation to estimate what the Q-factor would be if the stored RF wave energy results in an electric field of 4.7189E+04 volts per meter. It is very, very small. Small to the point of being nonsense at ~0.0007.

Correct me where I'm wrong, but the E field energy of the RF wave is given from w = epsilon_sub_o* E^2 where w is energy per unit volume, epsilon_sub_o = 8.85418782 × 10-12 m-3 kg-1 s4 A2 and the Quality factor is energy stored / energy lost per cycle. So I'm taking w = 28 watts with the unit volume of one and calculating much larger values than Fig. 14 shows.

Thank you for pointing out that the Q factor for the Cannae drive is not given. I had forgotten that.This is my understanding:

which is not too far from the COMSOL calculations (there is also an uncertainty due to the Volume)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~While for the tapered cavity

If you divide your

<<E field range from 80.4 to 184.8 Mv per metre>> by the actual square root of the angular frequency

Sqrt[ 2 Pi (1932.6*10^6 1/s) ] = 110195

one gets

E field range from 730 to 1677 Volts per meter (there is also an uncertainty due to the Volume)

Pardon me for quoting a volume of information but I think we can now discuss the real point of all this. That is, Rodal can since he has the math, I think.

As we know, the energy needed to create electron/positron pairs is 2*0.511 MeV which equals 1.6374 wattseconds. We now have some idea of the energy contained within the cavity and it is way more than enough to create e/p pairs. But is that energy properly oriented and concentrated enough for pair production? I found that the pair generally moves in the direction of the photon that created it (Wikipedia) but I don't know that any single photon contains sufficient energy, or how to calculate individual photon energy within the cavity.

Of course if pairs can be produced then we need to look very hard at Dr. White's theory for the thrust production.

I did look at the intensity of the RF wave in the dielectric of the Cannae device from the COMSOL figure.

Intensity=Power-watts/area (m^2), so area = power/average intensity = 28 Watts/RF power.I calculate the area = 9.474 square millimeter, so the power is quite concentrated.

Woodward has never suggested we can alter the rest mass of particles, but rather only of bulk mass items that store Mach Effects or mass fluctuations in the interatomic energy bonds. In fact, all bulk matter stores delta mass during deformation, since deformation changes the energy in these bonds and energy = mass X c^2.

Interesting, did not know that. Thanks.

Thus, Sciama's theory which was intended by Sciama only as an explanation of inertial mass, becomes in this interpretation of Woodward's theory a constitutive theory of matter, as words like "Woodward has never suggested we can alter the rest mass of particles, but rather only of bulk mass items that store Mach Effects or mass fluctuations in the interatomic energy bonds. In fact, all bulk matter stores delta mass during deformation, since deformation changes the energy in these bonds and energy = mass X c^2."

Constitutive laws cannot be determined theoretically. Theory (using for example frame-indifference, thermodynamics, symmetries, etc.) can only restrict, narrow down, the type of constitutive relation for a bulk material, but theory cannot prescribe what kind of constitutive equation a real material should have.

For example, there are countless definitions of rates of stress (Jaumann, Truesdell, Piola, Kirchoff, etc., and convected definitions) that satisfy frame-indifference. A Physicist cannot prescribe what definition of stress rate and strain-rate will lead to a linear constitutive relation for a given material in nature.

<< all bulk matter stores delta mass during deformation>> is an (strain-energy) Elastic constitutive prescription. Yet we know that the plain classical solid matter surrounding us is not necessarily elastic, including viscoelasticity (linear and nonlinear), as well as plasticity (softening and hardening with strain), etc. etc. and variations thereof (viscoelastic-plastic, viscoelastic-viscoplastic, etc.). A Physicist cannot select what the correct "constitutive" equation should be.

That can only be determined by experiment. There are plenty of constitutive theories that were found not to be followed by most materials. As a simple example, while a negative Poisson's ratio, as negative as -1, is allowed for an isotropic material by the theory of elasticity and by thermodynamic considerations, it is known that isotropic materials (not man-made) found in nature have a positive Poisson's ratio.

EDIT: Let's call the point at which constitutive statements are attached to Woodward's theory, a "W theory," such that "W theory" stands for the whole theory including any attached constitutive statement.

So even if one were to accept Woodward's theory on a theoretical basis, at the point that Woodward's theory becomes a constitutive theory, it does not follow that actual materials would have to behave as prescribed by "W theory" with a Buldrini factor >0. I think that Buldrini understood this and that's why he allowed his "fudge factors" to range all the way from zero (for a value of zero there is no Woodward effect).

Only experiments would be able to show whether they do or do not. However, if one were to accept "W theory" on a theoretical basis, and materials in nature are found not to obey it, the interesting possibility could still be raised whether such a "W theory" material could be eventually be man-made (to allow propellant-less drives) as for example now we are able to make isotropic materials with very negative Poisson's ratio that don't exist in nature. (The experiments that are trying to verify Woodward's effect now are limiting themselves to materials that are presently available for other uses, not materials that have been engineered by man first at the nano level and eventually at the molecular level with the only intent to maximize such a "W theory" effect. )

I gotta say IMHO of course, I am completely anti Machian and derivatives such as Sciama's take on inertia. Let me explain:

Mach's ideas come from a time where he didn't enjoy the benefit of anything QM. He didn't even believe that atoms exist I read somewhere.

Sciama mentions in his introduction accelerations in reference to the fixed stars. His ideas didn't enjoy the benefit of knowing the universe is expanding and accelerating.

For the life of me, I cringe when I read things such as local matter interacting with the distant matter of the universe, that kind of stuff. This isn't relevant anymore. How can we get instantaneous thrust if the action depends on a gravinertial field propagating at C.

What makes more sense to me are the various theories which explain the origin of inertia as quantum phenomena. Quantum effects are local, here, and now.

This emdrive thing has taken up a lot of my time lately, not so much as if or why it works. I have discovered that the jury is out on so many fundamental scientific concepts which I thought were nailed down, like inertia, origin or mass (not simply/only Higgs) and dark matter/energy. The dark energy/matter thing really bugs me. They were clearly invented to explain away inadequacies in theory attempting to explain observation. Instead of revising theory, more "crap" was piled on to fix it. Kinda like the games renormalization plays; card tricks. I think the current state of science is in bad shape in that theory has trumped observation. I get that it is important to spend time/money looking for new particles/gravity waves, etc. But I see little effort from mainstream science to go back and question itself when nothing new is found. One can ride a bunk theory for years and build a career of it. Then we end up with unfalsifiable theories like string theory or more particles like superpartners. Gravinertial fields are yet another invention to address something happening here and now that isn't explained by current accepted theory. Thus I am excited when I read things like "Anomalous Thrust Production from an RF Test Device" because if it really is true, it will really shake up the old tired paradigm I briefly ranted about above. It would do science a service if we would "play with what we got", instead of creating new theories to play with. GR hasn't let us down yet, but it is macro. There is a gap between macro and micro which could be filled in by modifying GR on its boundaries where appropriate, instead of treating it as complete. Einstein doesn't have an ego anymore. I admire Hawking for continually adjusting to the times.

I agree with aversion toward dark matter. I think you will enjoy Woodward book. I finish just 15%, but it is like course of the history SRT and GRT and in the same try to move forward and solve the problem inertia.

Pardon me for quoting a volume of information but I think we can now discuss the real point of all this. That is, Rodal can since he has the math, I think.

As we know, the energy needed to create electron/positron pairs is 2*0.511 MeV which equals 1.6374 wattseconds. We now have some idea of the energy contained within the cavity and it is way more than enough to create e/p pairs. But is that energy properly oriented and concentrated enough for pair production? I found that the pair generally moves in the direction of the photon that created it (Wikipedia) but I don't know that any single photon contains sufficient energy, or how to calculate individual photon energy within the cavity.

Of course if pairs can be produced then we need to look very hard at Dr. White's theory for the thrust production.

I did look at the intensity of the RF wave in the dielectric of the Cannae device from the COMSOL figure.

Intensity=Power-watts/area (m^2), so area = power/average intensity = 28 Watts/RF power.I calculate the area = 9.474 square millimeter, so the power is quite concentrated.

I think we calculated this a way back, with @notsureofit and @frobnicat and we all concluded that the 2 photon interaction in the microwave is way off from being able to make the virtual electron/positron pair real. I think that it takes a petawatt laser with picosecond period to be able to make the virtual electron/positron pair real. The frequency of the microwave is too low. That's why we eliminated the virtual electron/positron pair.

Dark matter axions remain a real possibility. I think @frobnicat is warning us that it is still off by 6 orders of magnitude (if I recall correctly). If @frobnicat is correct that would still be much closer than the ability of the microwave to make virtual electron/positron pairs real. And I have not seen @frobnicat's calculations yet.My concern with the dark matter axionic explanation is the density of axionic matter in our neighborhood: it appears to be too low according to that last paper we reviewed to justify the measured thrusts. But there are excellent people at Harvard that I recall expect a significantly larger density.

However, if one were to accept Woodward's theory on a theoretical basis, and materials in nature are found not to obey it

I think you're conflating two things: Woodward's theory (which describes what happens when certain things occur in a material) and the properties of the material (which describe how easily and/or efficiently those things can be forced to occur in it).

Woodward's theory itself has no efficiency terms. Those terms result from an attempt to map experimentally imposed parameters onto the quantities appearing in his equations. Since the electromechanical response of the material is what performs this mapping in real life, the efficiency terms represent the constitutive relations, which are not the Mach effect but mediate between the Mach effect and the attempt to force it to happen.

...

Assuming Woodward's theory is accepted for the sake of argument, saying a real-life material doesn't obey it is like saying a real-life material doesn't obey the law of gravity. A feather may not fall as fast as a brick, but there are other reasons for that.

Or perhaps a better example is a collision. Most real-life collisions don't appear to obey conservation of energy, until you account for dissipation of that energy in forms other than the bulk kinetic energy of the colliding objects.

Combining these two examples, bouncing a ball off the pavement and having it not quite come back up to the height it was dropped from does not mean the ball fails to obey either the law of gravity or the law of conservation of energy.

However, if one were to accept Woodward's theory on a theoretical basis, and materials in nature are found not to obey it

I think you're conflating two things: Woodward's theory (which describes what happens when certain things occur in a material) and the properties of the material (which describe how easily and/or efficiently those things can be forced to occur in it).

Woodward's theory itself has no efficiency terms. Those terms result from an attempt to map experimentally imposed parameters onto the quantities appearing in his equations. Since the electromechanical response of the material is what performs this mapping in real life, the efficiency terms represent the constitutive relations, which are not the Mach effect but mediate between the Mach effect and the attempt to force it to happen.

Assuming Woodward's theory is accepted for the sake of argument, saying a real-life material doesn't obey it is like saying a real-life material doesn't obey the law of gravity. A feather may not fall as fast as a brick, but there are other reasons for that.

I was explicitly addressing the comment <<"Woodward has never suggested we can alter the rest mass of particles, but rather only of bulk mass items that store Mach Effects or mass fluctuations in the interatomic energy bonds. In fact, all bulk matter stores delta mass during deformation, since deformation changes the energy in these bonds and energy = mass X c^2.">> which does not appear in your quote above.

The statement <<bulk mass items that store Mach Effects or mass fluctuations in the interatomic energy bonds>> for which the above was used as an analogy is another constitutive statement, specifically when invoking "interatomic bonds".

And concerning Buldrini, you yourself agree that << the [Buldrini] efficiency terms represent the constitutive relations>>.

I conflated the name "Woodward" for all of these things under the same "Woodward" umbrella: the Buldrini factors, the Stahl quotation, and the the fluctuation terms following from Sciama's derivation. Putting what Stahl writes under the same umbrella as Woodward, or Buldrini's theory under Woodward's umbrella maybe unfair but writing would otherwise become very awkward. I will write "W theory" from now on to encompass Woodward's formulation plus any (macroscopic or microscopic) constitutive statements that are attached to it.

"Advances are made by answering questions. Discoveries are made by questioning answers."

There went the evening.

And as an aside, adding to an earlier post of mine. My UVA math whiz read several of the Sciama papers at my suggestion, before asking me about the derivation. The disappointing remark that he made was, "I don't have the time to really dig into this."

Well, you edited what you wrote since I answered it. Concerning << Most real-life collisions don't appear to obey conservation of energy, until you account for dissipation of that energy in forms other than the bulk kinetic energy of the colliding objects.

Combining these two examples, bouncing a ball off the pavement and having it not quite come back up to the height it was dropped from does not mean the ball fails to obey either the law of gravity or the law of conservation of energy>>

Agreed that they do not fail to obey the law of gravity or conservation of energy. What they fail to obey is the (Cauchy-Hooke) law of perfect elasticity. What is normally called the impact "coefficient of restitution" is a constitutive law, it is usually due to plastic, viscoelastic or viscoplastic energy dissipation, which are all due to constitutive relations in which the body is not perfectly elastic. I have edited my previous original post that motivated your comment to now read "W theory" for Woodward's theory plus any constitutive statement (macroscopic or microscopic in nature) attached to it.

Well, you edited what you wrote since I answered it. Concerning << Most real-life collisions don't appear to obey conservation of energy, until you account for dissipation of that energy in forms other than the bulk kinetic energy of the colliding objects.

Combining these two examples, bouncing a ball off the pavement and having it not quite come back up to the height it was dropped from does not mean the ball fails to obey either the law of gravity or the law of conservation of energy>>

Agreed that they do not fail to obey the law of gravity or conservation of energy. What they fail to obey is the (Cauchy-Hooke) law of perfect elasticity. What is normally called the impact "coefficient of restitution" is a constitutive law, it is usually due to plastic, viscoelastic or viscoplastic energy dissipation, which are all due to constitutive relations in which the body is not perfectly elastic. I have edited my previous original post that motivated your comment to now read "W theory" for Woodward's theory plus any constitutive statement (macroscopic or microscopic in nature) attached to it.

Actually, your example is excellent to further discuss this. If you model the ball simplistically as a lumped mass, you can solve the problem with a "coefficient of restitution", but that is a "back of the envelope" solution, and not an engineering solution for the continuous body. If a company making tennis balls (or golf balls) wanted to improve the design of the balls they would conduct a more comprehensive solution: the solution of a number of differential equations, including the equilibrium equations, the strain-displacement equations and the (stress-strain) constitutive equations. The tennis ball (or the golf ball) exhibits large deformations during impact hence it is necessary to be careful to choose the stress and strain measures. Frame-indifference would restrict the choices. Energy conjugation (between stress, stress-rate, strain and strain-rate) would further restrict the choices. But there are still multiple choices that can be made. It turns out that to best characterize the constitutive behavior of the ball's material certain choices of stress, stress-rate, strain and strain-rate lead to simpler constitutive laws exhibited by materials in nature. Although the equilibrium equations and strain-displacement equations are not constitutive equations, the best choice for the stress and strain measures in the constitutive equations dictates what stress measure will appear in the equilibrium equation (it is in the equilibrium equation where gravity appears). Similarly for the strain-displacement equation. They are all affected by what measures are used. And the equilibrium equation is affected by the type of stress measure used, because different stress rate measures involve different quantities (spins or deformation gradients).

A similar issue appears as to what is known as the Abraham-Minkowski controversy: the Abraham-Minkowski controversy can only be resolved by experiments with real materials, it cannot be resolved theoretically. And if one adds "hidden momentum" terms as done by Shockley, one can use either Abraham's or Minkowski's formulation, but one of them is always more elegant (involving less terms) depending on what actual matter is being modeled.

Similarly, if one were to analyze a real material, not as a lumped mass, but as a continuum mechanics problem using a finite element analysis for example as proposed by Stahl, these issues appear concerning the complete "W theory": Woodward's theory plus constitutive statements. Particularly for real materials which in nature are anisotropic. Because, in a material one has to consider the stress tensor, not just forces.

After catching up on the past few pages, I'd be lying if I said I really understood any of what you're discussing. I don't suppose anyone has some good ideas on testable predictions from these theories?

Yes, the basic issue is whether rest mass can change at the particle level and not just as a rearrangement of kinetic energy.

I thought the lattice was composed of chemical bonds, which, when they heat up, among other things, vibrate more, sometimes to the breaking point. And if all these bonds are vibrating, and the various nucleii aren't moving, then I'm having a hard time with the "bulk acceleration" belief system.

If rest mass can change at all by microwave manipulation in these low energy ranges, it can change at the particle level, I would think.